The computation of the solution snapshots \(\mathfrak {u}_{\mu ^*}\)  via eq:twoscalesolution, however,
requires for each new \(\mu ^*\)  the recomputation of all corrector problems. For large
problems this may be computationally infeasible.
Thus, we combine our approach (Stage 2) with a preceeding prepartory step similar
to [1]}, where each corrector problem is replaced by an efficient ROM surrogate (Stage 1).
These ROMs are then used in the offline phase of Stage 2 to compute approximate solution snapshots
\(\mathfrak {u}_{\mu ^*}\) .
Again, Stage 1 is divided into ROM construction (sec:stage1rom), error estimation
(sec:stage1err), offline-online decomposition (sec:stage1of/on) and
construction of the reduced spaces (sec:stage1basisgen).
After a Stage 1 ROM is constructed, all associated fine-mesh data can be deleted.
In particular, all computations in Stage 2 are independent from size of \(\mathcal {T}_h\) .
